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FRM Part II · FRM Exam Part II · Future Value and Exposure

A bank simulates exposure on a 10-year cross-currency swap using 5,000 paths. The standard error of the estimated EE at the 5-year date is too large for the desk's tolerance. Which action most directly reduces the sampling error without changing the model assumptions?

Increasing the number of simulated paths, or using variance reduction such as antithetic variates, reduces sampling error because standard error shrinks with the square root of the path count, while leaving the model assumptions unchanged.

  1. AIncrease the number of paths or apply variance reduction such as antithetic variatesCorrect
  2. BShorten the time grid to year-end dates only
  3. CReplace the stochastic FX factor with its forward value
  4. DApply a floor of zero to simulated risk factors

Explanation

Monte Carlo standard error falls with the square root of paths, and variance reduction techniques lower it further for a given path count. Removing stochasticity or coarsening the grid changes the model and introduces bias rather than reducing sampling error.

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